Hi,
AxB = 0 means A=0. or B=0
so 2 solutions :
4x-3= 0
4x=3
x = 3/4
and x+2 = 0.
x= -2
solutions are : -2 +and 3/4
2 answers
1) -2
2) -3/4
How many solutions does the following equation have? -14(z-5)=-14x+70
Answer:
Infinite amount of solutions
Step-by-step explanation:
Parallel lines have no solution
Same lines have infinite solutions
Intersecting lines have 1 solution
Step 1: Write out equation
-14(x - 5) = -14x + 70
Step 2: Distribute -14
-14x + 70 = -14x + 70
Here we see that we have 2 exact same lines. Therefore, we have infinite amount of solutions.
Alternatively, we can plug in any number x and it would work. So then we would have infinite amount of solutions as well.
Assume x and y are two odd numbers and x/y is an integer.
Which of the following statements are true?
I. x + y is odd
2. xy is odd.
3. x/y is odd
4. x-y is odd
Answer:
Let us check these out one at a time:
1. x + y is odd. FALSE. The sum of 2 odd numbers is even.
2. xy is odd. TRUE. The product of 2 odd numbers is odd.
3. x/y is odd. TRUE. The ratio of 2 odd numbers is odd, if the ratio is an integer.
4. x - y is odd. FALSE. The difference of 2 odd numbers is even.
Only statements 2 and 3 are TRUE, so that makes (C) the correct answer.
The average of 4 numbers is 15 , the sum of 3 numbers is 14 what is the fourth number
Answer:
46
Step-by-step explanation:
(14+x)/4 = 15
14 + x = 60
x = 46
Answer:
46
Step-by-step explanation:
Let a to d be number 1 to 4 respectively.
15 = (a + b + c + d) / 4
(a + b + c + d) = 60 ------> total sum of the 4 numbers
Since the sum of 3 numbers (assuming a to c) is 14,
Fourth number (d) = 60 - 14
= 46
That's how I would do it, hope this helps :)
please Help with my area math question. I don't remember how to do it. multiply or add? and what is the answer to this?
Answer:
100 inches^3
Step-by-step explanation:
The volume of the back rectangle is
V = l*w*h
V = 8*5*1 = 40 inches ^3
The volume of the front rectangle is
V = 6*2*5 = 60 inches^3
Add the volumes
40+60 = 100 inches^3
[tex](y - 1) log_{10}(4?) = log_{10}(16?) [/tex]
find the value of y
Answer:
3Step-by-step explanation:
Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;
[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]
Open the bracket
[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]
Hence the value of y is 3
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
At the beginning of March, a store bought a fancy watch at a cost of $250 and marked it up 20%. At the end of the month, the fancy watch had not sold, so the store marked it down 10%. What was the discounted price?
Answer:
$270
Step-by-step explanation:
Price after markup was 1.20($250) = $300
Price after discounting: (1.00 - 0.10)($300) = $270
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = 8x3 − 12x2 − 48x
Answer:
(2, -1)Step-by-step explanation:
Given the function f(x) = 8x³ − 12x² − 48x, the critical point of the function occurs at its turning point i,e at f'(x) = 0
First we have to differentiate the function as shown;
[tex]f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\[/tex]
[tex]Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1[/tex]
Hence the critical numbers of the function are (2, -1)
If a faucet drips 2ml of water every second, how much water will it spill waste in 2 days?
Answer:
[tex]\boxed{345,600 mL}[/tex]
Step-by-step explanation:
Hey there!
Well first we need to find the amount of seconds in a day,
24hrs in a day * 60 min in an hour
= 1440 minutes in a day
1440 min • 60 secs in a minute
= 86,400 seconds in a day
So now we do 2*86400 = 172800
172800 mL in a day
172800 * 2
= 345600 mL in 2 days
Hope this helps :)
marc mixes blue and yelow paint to ,ake green he has 14 cans blue 20 cans of yellow . he wants green color so one day 1 he mixes 4 blue 6 yellow day 2 he mixes 6 can blue 9 yellowwhats the highest number of cans each color marc can mix to mzke the same shade of green on day 3
Answer:
2 c an of blue and 5 can of yellow
Step-by-step explanation:
Two math classes took the same quiz. The scores of 10 randomly selected students from each class are listed below. • Sample of Class A: 75, 80, 60, 90, 85, 80, 70, 90, 70, 65 • Sample of Class B: 95, 90, 85, 90, 100, 75, 90, 85, 90, 85 Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in Class A compared to all the students in Class B? Explain your reasoning to justify your answer.
Answer:
Step-by-step explanation:
First you have to find the medians which is when you put the numbers in number order and find the one in the middle.
Class A: 60,65,70,70,75,80,80,85,90,90
=77.5
Class B: 75,85,85,85,90,90,90,90,95,100
=90
That the class B is more advanced, and they probably studied.
Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 2.
Answer:
[tex]\Large \boxed{\sf \bf \ \ 2(x-4)^3(x+2)^2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
Construct a polynomial function with the following properties...
... fifth degree
It means that the polynomial can be written as below.
[tex]a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0 \ \text{ with }a_5\text{ different from 0}\\\\\text{ or } k(x-x_1)(x-x_2)(x-x_3)(x-x_4)(x-x_5) \\\\ \text{ with k different from 0 and } (x_i)_{1\leqi\leq 5 } \text { are the roots.}[/tex]
... 4 is a zero of multiplicity 3
We can write the polynomial as below.
[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)=k(x-4)^3(x-x_4)(x-x_5)[/tex]
... −2 is the only other zero
Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.
[tex]k(x-4)(x-4)(x-4)(x-x_4)(x-x_5)\\\\=k(x-4)^3(x-(-2))(x-(-2))\\\\=k(x-4)^3(x+2)^2[/tex]
... leading coefficient is 2.
Finally, it means that k = 2 and then the polynomial function is:
[tex]\large \boxed{2(x-4)^3(x+2)^2}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
heeeeeeeeelpppppppppppp
Answer:
1). x = 2.67 units
2). x = 4.80 units
3). x = 6.00 units
Step-by-step explanation:
1). By applying Pythagoras theorem,
Hypotenuse² = [Leg(1)]² + [leg(2)]²
12² = x² + b² [Let the base of both the triangles = b units]
144 = x² + b² ------(1)
Similarly, 13² = (x + 3)² + b²
169 = x² + 6x + 9 + b²
169 - 9 - 6x = x² + b²
160 - 6x = x² + b² ------(2)
From equation (1) and (2)
144 = 160 - 6x
6x = 160 - 144
x = [tex]\frac{16}{6}[/tex]
x = 2.67 units
2). By applying Pythagoras theorem,
10² = x² + h² [Let the height of the triangle = h]
100 = x² + h² ------(1)
13² = (2x)² + h²
169 = 4x² + h² -----(2)
By substituting equation (1) from equation (2),
169 - 100 = (4x² + h²) - (x² + h²)
69 = 3x²
x² = 23
x = √23
x = 4.795
x ≈ 4.80 units
3). By applying Pythagoras theorem,
9² = x² + h² [Let the height of the triangle = h units]
81 = x² + h² ------(1)
7² = (x - 4)² + h²
49 = x² + 16 - 8x + h²
49 - 16 = x² + h² - 8x
33 + 8x = x² + h² -------(2)
From equation (1) and (2)
81 = 33 + 8x
8x = 48
x = 6.00 units
2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?
Answer:
Percentage of home team supporters =65%
Percentage of visiting team supporters =35%
Step-by-step explanation:
Total attendees=2,000 people
Home team supporters=1,300
Visiting team supporters=700
What percentage of people attending supported the home team?
Percentage of people attending who supported the home team = home team supporters / total attendees × 100
=1,300/2,000 × 100
=0.65 × 100
=65%
Visiting team supporters = visiting team supporters / total attendees
× 100
=700/2000 × 100
=0.35 × 100
=35%
Alternatively,
Visiting team supporters = percentage of total attendees - percentage of home team supporters
=100% - 65%
=35%
Find the surface area of the solid given the net.
Answer:
288
Step-by-step explanation:
Area of two triangles=2(½bh)
=bh
=8×6
=48
For the rectangles=lb + lb +lb
l(b+b+b)
=12(8+6+6)
=12×20
=240
Total area=240 +48=288
Find the length of FT¯¯¯¯¯¯¯ A. 77.71 B. 72.47 C. 56.84 D. 49.42
Answer:
D, 49.42
Step-by-step explanation:
ΔVFT=180-90-43=47
formula
a/sin A = b/sin B/ = c/sin C
So,
FV/sin90=53/sin47
FV=72.4684
FT=√(72.4684)^2-(53)^2
FT=49.4234
Ans:D
The length FT in the given right-angle triangle is 49.42.
So option D is the correct answer.
We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.
In the triangle, we see that TV = 53 and ∠ FVT = 43°
We will find the length FT by using Pythagoras theorem or trigonometric identities.
What are trigonometric functions?
There are some commonly used trigonometric identities:
SinФ = Perpendicular / hypotenuse
Cos Ф = Base / hypotenuse
Tan Ф = Perpendicular / Base
We will use Tan Ф = Perpendicular / Base to find the length FT.
Because we need to use trigonometric identities that have TV and FT.
Tan Ф = FT / TV
Tan 43° = FT / 53
FT = Tan 43° x 53
FT = 0.932515 X 53
FT = 49.42
Thus we got FT = 49.42 using the tan function.
Learn more about trigonometric functions here:
https://brainly.com/question/14746686
$SPJ2
solve the following inequalities 7 x minus 5 / 8 x + 3 >4
Answer:
[tex]x> \frac{8}{51} [/tex]
Step-by-step explanation:
[tex]7x - \frac{5}{8} x + 3>4[/tex]
Bring constants to one side, simplify:
[tex] \frac{51}{8} x>4 - 3 \\ \frac{51}{8} x>1 \\ x>1 \div \frac{51}{8} \\ x>1 \times \frac{8}{51} \\ x> \frac{8}{51} [/tex]
*Note that the inequality sign only changes when you divide the whole inequality by a negative number.
Answer:
[tex]x>\frac{8}{51}[/tex]
Step-by-step explanation:
[tex]7x-\frac{5}{8}x+3>4\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}\\7x-\frac{5}{8}x+3-3>4-3\\\mathrm{Simplify}\\7x-\frac{5}{8}x>1\\\mathrm{Multiply\:both\:sides\:by\:}8\\7x\times \:8-\frac{5}{8}x\times \:8>1\times \:8\\\mathrm{Simplify}\\56x-5x>8\\51x>8\\\mathrm{Divide\:both\:sides\:by\:}51\\\frac{51x}{51}>\frac{8}{51}\\\\x>\frac{8}{51}[/tex]
I hope it helps :)
The perimeter of a rectangular Garden is 80 feet the garden is three times as long as it is wide the system of equation can be used to find the width in the length
Answer:
10 wide 30 long
Step-by-step explanation:
1. Start guess and check.
2. When you get to 10 follow this:
10x3=30. 30+30+10+10=80
80=80
The owner of a small hardware store employs three men and three women. He will select three employees at random to work on Christmas Eve. Find the probability that exactly two men (and one woman) will be selected to
work (2DP)
Answer:
Step-by-step explanation:
This is a hypergeometric distribution
[tex]\frac{{3\choose2}*{3\choose1}}{{6\choose3}}[/tex]=.45
What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
Step-by-step explanation:
(5+(-4))/2 = 1/2 or 0.5
(-7 + 6)/2 = -1/2 or -0.5
the solution is D
(0.5, -0.5)
The vertices of a quadrilateral are listed below. A(8,-1), B(13,-1), C(18,-7), D(8,-7) Which of the following is the strongest classification that identifies this quadrilateral? A. The quadrilateral is a rhombus. B. The quadrilateral is a trapezoid. C. The quadrilateral is a square. D. The quadrilateral is a rectangle.
Answer:
A
Step-by-step explanation:
Because of we pur all the points on the Cartesian plane and we "connect" all the points comes a rhombus
SORRY FOR MY BAD ENGLISH BUT I AM ITALIAN
Rewrite 3.16 as a fraction (the 6 is repeating)c
[tex]3\frac{16}{99} = \dfrac{313}{99}= 3.161616161616.....[/tex]
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
Use the listing method to represent the following set. Hurry plz!!!
[tex]\\ \sf\longmapsto \left\{x|x \epsilon I,x\leqslant 3\right\}[/tex]
Here x belongs to set of Integersx is less than or equal to 3In listing
[tex]\\ \sf\longmapsto \left\{\dots,0,1,2,3\right\}[/tex]
PLEASE HELP i’ll give brainliest to best and correct answer
Step-by-step explanation:
|- 9| + |- 3|
9 + 3
12
I hope this answers your question
Part E
1e. Subtract the binomial 12y2 – 4y3 from the trinomial 7y - 2y3 + 5y2
Answer:
2y^3-7y^2+7y
Step-by-step explanation:
7y - 2y^3 + 5y^2 - ( 12y^2 – 4y^3)
Distribute the minus sign
7y - 2y^3 + 5y^2 - 12y^2 + 4y^3
Combine like terms
2y^3-7y^2+7y
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
TI
(S.
(3.1, 0.3) and (2.7, -4.9)
Th
(Rd
Answer:
5.215 units (rounded up to three decimal places)
Step-by-step explanation:
To find the distance between points (3.1 , 0.3) and (2.7, -4.9)
We use the Pythagoras Theorem which states that for a right triangle of sides a,b and c then;
a² + b² = c² , Where c is the hypotenuse.
In our case, the distance between the two points is the hypotenuse of triangle formed by change in y-axis and change in x-axis.
The distance (hypotenuse) squared = (-4.9 - 0.3)² + (2.7 - 3.1)² = 27.04 + 0.16 = 27.2
Hypotenuse (the distance between) = [tex]\sqrt{27.2}[/tex] = 5.215 units (rounded up to three decimal places)
Suppose P( A) = 0.60, P( B) = 0.85, and A and B are independent. The probability of the complement of the event ( A and B) is: a. .4 × .15 = .060 b. 0.40 + .15 = .55 c. 1 − (.40 + .15) = .45 d. 1 − (.6 × .85) = .490
Answer: a. 0.4 × 0.15 = 0.060
Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.
For P(A):
P(A') = 1 - 0.6
P(A') = 0.4
For P(B):
P(B') = 1 - 0.85
P(B') = 0.15
To determine probability of A' and B':
P(A' and B') = P(A')*P(B')
P(A' and B') = 0.4*0.15
P(A' and B') = 0.06
Probability of the complement of the event is 0.060
Which expression is equivalent to sqrt of (6x^5 z)^3/ 4x^4 z^2
Answer:
[tex]\frac{(6x^{5}z) ^{3} }{4x^{4} {z}^{2} } = \frac{216 {x}^{15}z^{3} }{4 {x}^{4} {z}^{2} } = \frac{4x ^{4} {z}^{2} (54x ^{11}z) }{4 {x}^{4} {z}^{2} } = 54 {x}^{11} z[/tex]
I hope I helped you^_^
the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.
Answer:
[tex]4000(1.023)^t\\\\[/tex]
Step-by-step explanation:
Using this exponential growth equation we can get an equation that models the situation.
A= Principal Amount
R= Rate of Growth
T= Amount of time
[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]
[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]